- #1

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My teacher wrote that:

"The set has no interior points, and neither does its complement, R\Q" where R refers real

numbers and Q is the rationals numbers.

why can't i find an iterior point?

thanks,

Omri

- Thread starter omri3012
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- #1

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My teacher wrote that:

"The set has no interior points, and neither does its complement, R\Q" where R refers real

numbers and Q is the rationals numbers.

why can't i find an iterior point?

thanks,

Omri

- #2

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Let q be an arbitrary rational number. Does there exist a neighborhood of q that is a subset of Q?

- #3

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How about the fact that I can squeeze a real number between any two arbitrary points of Q?

- #4

HallsofIvy

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Irrelevant. Do you mean anHow about the fact that I can squeeze a real number between any two arbitrary points of Q?

- #5

HallsofIvy

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So "the set" is Q. For p to be an interior point of Q, there must exist an interval around p, \(\displaystyle (p-\delta, p+\delta)[/quote] consisting entirely of rational numbers. For p to be an interior point of R\Q, the set of irrational numbers, there must exist an interval [itex](p- \delta, p+ \delta)[/itex]] consisting entirely of irrational numbers. There is NO interval of real numbers consisting entirely of rational number or entirely of irrational numbers.\)

My teacher wrote that:

"The set has no interior points, and neither does its complement, R\Q" where R refers real

numbers and Q is the rationals numbers.

why can't i find an iterior point?

thanks,

Omri

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- #6

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- #7

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I'm sorry but the statement (as i guess you already assume) was:

"The set

thanks

Omri

- #8

HallsofIvy

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Yes, that was essentially what everyone was assuming.

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